Imagine a wire with uniform circular cross-sectional area and length l. It is being pulled at both ends with a horizontal force that is equal and opposite to each other. The wire obeys Hooke's law up to breaking. (1) How do we calculate the work done by the wire if both sides of the wire extend by 2e (i.e. an extension of "e" at each end of the wire)? (2) How do I explain the difference between the cancellation of the vector components of each force and the fact that the wire still extends? (3) What is the most proper way of writing down the mathematical working of the extension of the wire? On a side note, (4) How does the energy stored in the wire change, then? (5) Also, in what cases are we supposed to assume that the cross-sectional area remains approximately the same and when do we not? (6) Is the approximation e^2 ≈ 0 necessary in this case when I'm calculating the energy stored in the wire? Thank you for your help.